What helps you visualize dimensions?

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An interesting question came up the other day. Someone asked how to visualize the tinier dimensions, and though I like to think that I can, it was pretty hard to put it into words. Here’s my attempt. Not saying it’s right, just saying it works for me. I’d be very interested to see what works for others.

First, two simple principles: (A) For any given dimension, treat the next highest dimension as its “time.” (B) Mapping out how the state of a given dimension changes over “time” gives you a visualization of the next highest dimension.

To make it easier, I start from the smallest and work highest. Going the other way hurts my head.

To keep it short, I’ll run through 8 or 9 dimensions. The three dimensions we live in are numbers 4, 5 and 6. (Dimension 6 is the really interesting one to me.)

0. Start with a singularity of zero dimension. It’s just a reference point, such as the intersection of two lines or three planes. It’s a point.

1. Map out how that point changes over time. You now have a 1-dimensional line.

2. Map out how that line changes over time. You now have a 2-dimensional plane.

3. Map out how that plane changes over time. You now have a 3-dimensional space.

4. Map out how that space changes over time. Imagine each new instance of that space as an infinitesimal point. You now have a 4-dimensional line, with each point on that line being how the entire 3-dimensional space was at any given moment.

5. Map out how that 4-dimensional line changes over its time, and you now have a 5-dimensional plane.

6. Map out how that 5-dimensional plane changes over its time, and you now have a 6-dimensional field. Think of this as what we normally think of as the 3-dimensional space we experience.

Each infinitesimal point in that 6-dimensional field is a 3-dimensional space of its own. This helps me visualize how nearby points in a field react as they do -- they’re not different things spookily acting at a distance, but are instead just the same 3-dimensional sphere (or whatever) reacting to something over its “time.”

7. Map out how that 6-dimensional field changes over time, and you now have a 7-dimensional thing that we refer to as “spacetime.”

8. I need another dimension on top of that, an 8th dimension, for a sort of Bohm pilot wave that helps me imagine a photon trying out various pathways in its phase space, outside of time, perhaps interfering with each other as in a 2-slit experiment, then traveling down one of those pathways in the spacetime we experience. (See discussion at https://www.physicsforums.com/showthread.php?t=148050&page=5 )

Like I said, I’m not in any way saying this is RIGHT, just that it helps me deal with the concepts. I’d love to hear what works for others.
 

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